FINITE-TEMPERATURE MANY-BODY THEORY WITH THE LIPKIN MODEL

We have compared exact numerical results for the Lipkin model at finit e temperature with Hartree-Fock (HF) theory supplemented by the partic le-particle hole-hole ring diagrams and with the static path approxima tion (SPA). In the simplest version of the Lipkin model the HF approac h shows a ''phase transition'' which is absent in the exact results an d in the SPA. For more realistic cases, HF is quite accurate at low te mperature, but less so at high temperature. In contrast the SPA appear s to be highly satisfactory for high temperatures, but less accurate a t low temperature. The effect of the ring diagrams is small at low tem perature, but it is more significant at high temperature where a moder ate improvement to HF brings the results into closer agreement with th e exact calculations.